Question

Quantities p, q, r, s are measured with errors 3%, 2%, 3% and 1%. $A = \frac{pq^{2}{r^{3}s}$. The percentage error in A is}

• A. 17%
• B. 12%
• C. 18%
• D. 19%

Hint:

Always multiply the percentage error of a quantity by its exponent in the formula.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need to find the total percentage error in a derived quantity based on the individual errors of its components.

Step 2: Key Formula or Approach:
For a formula \( X = \frac{a^m b^n}{c^k} \), the maximum fractional error is:
\[ \frac{\Delta X}{X} = m \frac{\Delta a}{a} + n \frac{\Delta b}{b} + k \frac{\Delta c}{c} \]

Step 3: Detailed Explanation:
Given formula: \( A = \frac{p q^2}{r^3 s} \)
Percentage error in A is:
\[ %A = 1 \cdot (%p) + 2 \cdot (%q) + 3 \cdot (%r) + 1 \cdot (%s) \] Substituting the given values (\( %p = 3, %q = 2, %r = 3, %s = 1 \)):
\[ %A = 1(3%) + 2(2%) + 3(3%) + 1(1%) \] \[ %A = 3% + 4% + 9% + 1% \] \[ %A = 17% \]

Step 4: Final Answer:
The percentage error in 'A' is 17%.